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Error Detection and Correction

This document discusses different methods for error detection in digital communications, including parity checks, cyclic redundancy checks (CRC), and Hamming codes. Simple parity checks can detect single-bit errors but not burst errors affecting an even number of bits. CRC uses a polynomial approach to detect most burst errors of length less than the polynomial degree. Hamming codes provide even stronger error detection by encoding extra redundant bits to allow detection and correction of multiple simultaneous bit errors.

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Seravana Kumar
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151 views22 pages

Error Detection and Correction

This document discusses different methods for error detection in digital communications, including parity checks, cyclic redundancy checks (CRC), and Hamming codes. Simple parity checks can detect single-bit errors but not burst errors affecting an even number of bits. CRC uses a polynomial approach to detect most burst errors of length less than the polynomial degree. Hamming codes provide even stronger error detection by encoding extra redundant bits to allow detection and correction of multiple simultaneous bit errors.

Uploaded by

Seravana Kumar
Copyright
© Attribution Non-Commercial (BY-NC)
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PPTX, PDF, TXT or read online on Scribd
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Types of Errors

Single-bit Error
Burst Error

Redundancy

Error Detection Methods

Simple Parity Check

Examples
Suppose the sender wants to send the word WORLD.

In ASCII, the five characters are coded as:


1110111

1101111
O

1110010
R

1101100
L

1100100
D

Actual Bits Sent:

11101110

11011110

11100100

11011000

11001001

Examples
Suppose the word WORLD is corrupted during

transmission
11111110 11011110 11101100 11011000 11001001 7 6 5 4 4 Here receiver knows that data is corrupted, discards them and asks for retransmission

Performance
This will work well for single bit as well as burst errors

as long as total number of bits changed is odd This will not work well when the total number of bits changed is even.

Two-Dimensional Parity Check

Performance
Two-dimensional parity check increases the likelihood

of detecting burst errors If 2 bits in data unit are damaged and two bits in exactly the same positions in another data are also damaged, the checker will not detect an error Ex: 11110000 and 11000011 changed: 01110001 and 01000010

Cyclic Redundancy Check

Cyclic Redundancy Check


Generating CRC

Cyclic Redundancy Check

Cyclic Redundancy Check


Divisor in the CRC generator is represented as

algebraic polynomial instead of 1s and 0s Reason:


Short Mathematically Proved

Performance of CRC
CRC can detect all burst errors that effect odd number

of bits CRC can detect all burst errors of length less than or equal to the degree of the polynomial CRC can detect, with very high probability, burst errors of length greater than the degree of the polynomial

Checksum
It is the third mechanism for error detection which is

also based on redundancy

Checksum
Example: Data: 10101001 00111001 Sender: The numbers are added using ones complement arithmetic

Hamming Code

Hamming Code

Hamming Code

Hamming Code

Hamming Code

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